Conformal transformation from 2 circles to 2 line segments

Question

thank you very much for creating this website and allow people to ask questions here. This is my question, I want to know if it is possible to find a conformal transformation that maps the inside of the unit circles to their respective line segments as follows: There are 2 circles in the z-plane, both circles have a unitary radius. The first circle is centered at the origin of the z-plane (0,0). The second circle is placed bellow the first circle at a distance of 2ih.The variable h is a real and positive number, is a constant and can be any number. The second circle is centered at the point (0,-2ih).I want to know if it is possible to find a conformal transformation that maps the inside of the first unit circle to a line segment v=0 between u=-1 and u=1 in the w-plane; and the second circle is mapped to its respective line segment v=-2ih' between u-1 and u=1. The variable h' is another variable that represents any constant real and positive number, however it can be different or the same value as h. I have been working in this problem for a long time, but my knowledge of conformal mapping is not so good, I would appreciate any help, Thank you very much.